Question

triangle abc is an isosceles right triangle. what is the measure of one base angle? \
\\( 30^{\circ} \\) \
\\( 45^{\circ} \\) \
\\( 60^{\circ} \\) \
\\( 90^{\circ} \\)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Identify right and equal angles

In an isosceles right triangle, one angle is \(90^\circ\) (right angle), and the other two angles (base angles) are equal. Let each base angle be \(x\).

Step3: Set up equation and solve

Using angle sum: \(90^\circ + x + x = 180^\circ\)
Simplify: \(90^\circ + 2x = 180^\circ\)
Subtract \(90^\circ\): \(2x = 90^\circ\)
Divide by 2: \(x = 45^\circ\)

Answer:

\(45^\circ\) (corresponding to the option with \(45^\circ\))